Kilogram as a relic in physics: - In search of a universal definition of the unit of mass -  

Malgorzata Worek RWTH Aachen University

Habilitation Talk, 14 July 2015, RWTH Aachen University 1  

National standard K20 stored in USA

Instead of Introduction…

  Activities of every day life affected directly or indirectly by mass measurements

  Direct or indirect impact on trade and commerce

  Impact the scientific community

  Ensure equity and equivalence in trade and manufacturing at the national and international levels

Uniform standards are needed !!!

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History Lesson…   The metric system was developed from 1790 onwards by French scientists commissioned by Louis XVI to create a unified and rational system of measures   Original definition from 7 April 1795 proposed by French National Assembly

The kilogram is the mass of one cubic decimeter of water at the temperature of maximal density (4°C)

  22 June 1799 – an all-platinum prototype (the Kilogram of the Archives) was manufactured and deposited in the Archives of the French Republic in Paris

The kilogram is the mass of the Kilogram of the Archives

  20 May 1875 - The International Bureau of Weights and Measures (BIMP) & The International Committee for Weights and Measures (CIPM)   Followed by establishing foundations of the International System of Units (SI)

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The Kilogram of the Archives  

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Le Grand K   International prototype of the kilogram (IPK) is an artifact whose mass defines at present the SI unit of mass (definition established in 1901)

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram

  Sanctioned in 1889 - Le Grand K - KIII   Cylinder with diameter and height of about 39.17 mm   Made of 90% platinum and 10% iridium      Stored in a vault at BIPM outside Paris for more than 120 years with six copies   Kept in air under three bell jars   The basis for more than 80 copies distributed around the world

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Pt‑10Ir

Vault located in the basement of the BIPM’s Pavillon de

Breteuil in Sèvres

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National prototype of the kilogram Germany (52, 55 and 70)

  Maintained under two bell jars at standard ambient conditions at the German National Metrology Institute in Braunschweig

  About every 10 years tested against the international prototype at the BIPM

  The secondary standards of stainless steel are compared with the national prototype once a year

The national prototype of the kilogram of Germany - No. 52 – 7  

What about Other Units of Mass ?

  The avoirdupois (or international) pound is used in both the Imperial system and U.S. customary units

  Defined as exactly 0.45359237 kg, making one kilogram approximately equal to 2.2046 avoirdupois pounds

  Other traditional units of mass around the world are also defined in terms of Kg

The IPK the primary standard for virtually all units of mass on Earth !!!

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  The unit of mass is only available at the BIPM

  Prototypes serving as national standards of mass must be returned periodically to the BIPM for calibration

  High costs: BIPM: ~ 70 employees, budget ~ 106 EUR/year

  Transport: constantly in danger of being damaged or destroyed

  Long-term instability of the unit of mass ~ 30-50 µg over the last century

  1999: BIMP - Recommendation for redefinition of kilogram in terms of fundamental physics constants - Planck constant h

Problems…  

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  Simultaneous recalibration of all National Prototypes of the Kilogram at BIPM   1889, 1939 - 1946, 1988 – 1992   Mass standards are stored in ambient air   They accumulate contaminants and must be cleaned   Surface contamination approaching 1 µg per year for national prototypes

  1939 - 1946: "the BIPM cleaning method”   rubbing with chamois cloth that has been soaked in a mixture of equal proportions of diethyl ether and ethanol   followed by steam cleaning with bi-distilled water   7 - 10 days to stabilize before calibration

  New definition since 1989:

Periodic verification  

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram just after cleaning and washing using BIPM method

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Mass Measurements    Balance reading = the difference between the gravitational and buoyant forces   Balance reading allows for the determination of the mass value   Reference R & unknown X

  mR, mX, VR, VX – mass and volume for the reference R and the unknown X   CR and CX – balance reading for the reference R and the unknown X   ρa – assumption that air density does not change during the measurement   The simplest and most fundamental mass measurement process

C = (CR −CX)

mR − ρaVR = CR

mX − ρaVX = CX

mX = mR − ρa(VR −VX)−C

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Overview of Mass Standards  

All of these standards are made from Pt-Ir (90% to 10%) 2013-2014 a new campaign - after ~ 22 years

Masses of BIMP standards are compared to each other and to the IPK

Metrologia 52 (2015) 310

Mass losses of the IPK

Mass losses of the IPK and its six official copies after cleaning and washing Contamination rates 0.6 – 0.8 µg/yr -1

Metrologia 52 (2015) 310

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Mean: -15 µg

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Stability of the IPK  Metrologia 52 (2015) 310

Evolution in mass: results of comparisons between the official copies and the IPK some divergence with time 50 µg in 100 years

On average a change by only 1 µg since the 3rd PV in 1991

Mass increase of the IPK

Mass increase of the IPK and its six official copies after the last cleaning and washing operation

Metrologia 52 (2015) 310

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Problems Continue…  

As of 2015 the kilogram remains the only SI base unit defined by an artifact

  Environment effects, mechanical wear and surface effects like adsorption & absorption of atmospheric contamination results in IPK gaining mass over time   Instabilities in definition of kg propagate to other SI base units…

  Precision of comparisons can be done at the level 10-10 - 10-12 !!!   Limitation lies within the artifact definition itself

Dependence of the SI on the IPK   The instability in the definition of the kilogram propagates to other SI base units that are tied to the kilogram

  The seven SI base units and their interdependency   kelvin (temperature)   second (time)   metre (distance)   kilogram (mass)   candela (luminous intensity)   mole (amount of substance)   ampere (electric current)

  SI derived units   Unit of force - newton [N]   Unit of pressure - pascal [Pa]   Unit of energy - joule [J]   Unit of power – watt [W]   Units of electricity – coulomb [C], volt [V], tesla [T], weber [Wb], ohm [Ω]   …

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Towards a New Definition of Kg   Long term solution:

  Kg defined with respect to universal constant of nature   Practical realization of Kg that can be reproduced in different laboratories   Specifications/Conditions

At least 3 experiments with relative standard uncertainties below 5 × 10-8

One of these results should have uncertainty below 2 × 10-8

Only two types of experiments relevant: Watt balance & Avogadro project

  Experimental Groups:   NIST – National Institute of Standards and Technology, USA   NPL – National Physical Laboratory, UK   NRC - Institute for National Measurements Standards, Canada   CODATA – Committee on Data for Science and Technology, France   METAS – Federal Institute of Metrology, Switzerland   IAC – International Avogadro Coordina3on  Project – France, Italy, Belgium, USA, Australia, Japan, UK, Germany

Metrologia 51 (2014) R21

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The watt balance   Proposed by B. P. Kibble in 1975   Consists of two parts to relate mechanical power to electrical power both in watts   Electrical power can be defined in terms of quantum effects

Force mode based on Lorentz Force

Fm – gravitational force on a mass m Fe – electromagnetic force generated by a coil currying a current I in the magnetic field B – magnetic field

L – wire length

Fm = Fe

mg = BLI

Metrologia 51 (2014) S 5 Metrologia 51 (2014) S 15

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The watt balance

  Connection from mass to h via electrical quantities & quantum physical effects

  Josephson effect & Quantum Hall effect

Velocity mode based on Faraday’s Law of Induction

v – vertical speed of a coil in a magnetic field B V - induced voltage L – coil (wire) length

Induced voltage related to velocity via flux integral BL

V = BLv

mg v = V I

Metrologia 51 (2014) S 5 Metrologia 51 (2014) S 15

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Josephson Effect   Observed in Josephson junctions (JJ)

  2 superconductive materials separated by non-superconducting barrier

  At superconducting temperatures while irradiating the junction with an electromagnetic field at microwave frequency f a current is forced through this junction

  … and a voltage will develop across the junction

  Josephson constant   One junction delivers small voltage ~ 37 μV   Practical voltage standard: 250 000 junctions connected in series on a single chip   Any voltage up to 10 V with uncertainty nV

V =h

2ef ≡ K−1

J f

KJ = 2e/hsingle junction 6 μm × 20 μm

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Quantum Hall Effect   Special case of Hall effect for 2-dimensional electron system   Current currying conductor immersed in a magnetic field   Voltage VH occurs perpendicular to B and I   At low temperatures (at liquid helium temperature T =4.2 K) and high magnetic fields (several tesla) Hall resistance RH is quantized

  von Klitzing constant   100 Ω precision resistor with relative uncertainty 10-9

RK = h/e2

RH =VH

I=

1

i

h

e2≡ 1

iRK

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Combining Two Effects   Instead of directly measure P=V I current I driven through precisely calibrated resistor R producing voltage drop VR

  Both voltages V and VR are measured by comparing to Josephson voltage standard   Expressed in terms of f and KJ

  Resistance is measured by comparing to a quantum Hall resistance standard   Expressed in terms of RK

gravimeter &

interferometer P = VI =

VVR

R= mgv

P = mgv = Cf1 f2h2

4e2e2

h= C

f1 f24

h

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In Practice

  Different system of units used for electrical measurements since 1990   Called conventional electrical units   based on the so-called "conventional values" of Josephson constant and von Klitzing constant & agreed by the International Committee for Weights and Measures (CIPM) - KJ-90 = 483 597.9 GHz V-1 and RK-90 = 25 812. 807 Ω (exact)

  All electrical measurements calibrated in conventional units   By comparing electrical power in conventional units to mechanical power in SI units h can be determined   h90 is the conventional value of the Planck constant

Metrologia 51 (2014) S 5 Metrologia 51 (2014) S 15

(mgv){SI}(VI){90}

=W{90}

W{SI}=

h

h{90}h = h90

(mgv){SI}(VI){90}

h90 ≡ 4

K2J−90 RK−90

= 6.626 068 854 · · ·× 10−34Js

Results

NIST: h = 6.626 069 79 (30) × 10－34 J s Relative uncertainty 4.5 × 10－8

NRC: h = 6.626 070 34 (12) × 10－34 J s Relative uncertainty 1.8 × 10－8

Metrologia 51 (2014) S 5 Metrologia 51 (2014) S 15

h = h90R{90}

V{90} VR {90}mgv

h90 ≡ 4

K2J−90 RK−90

  Measured values of the Planck constant   Lowest uncertainty 1.8 × 10－8 reported to date (March 2014)    

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Metrologia 48 (2011) S1 PRL 106 (2011) 030801

Avogadro Project

  Avogadro constant NA links atomic and macroscopic properties of matter   Counting atoms in 1 kg single-crystal spheres made of 28SI (silicon-28)   Free of imperfections, mono-isotopic and chemically pure   X-ray crystallography   Avogadro constant - ratio of the molar volume Vmol to atomic volume Va

Silicon unit cell

n =8 is the number of atoms per unit cell of volume Vcell

of silicon crystal 28SI

NA =Vmol

Va

Va =Vcell

n=

a3

n

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Metrologia 48 (2011) S1 PRL 106 (2011) 030801

Avogadro Project   Molar volume Vm

  NA measurement based on

  Molar mass via gas mass spectrometry   X-ray interferometer measures a   Density from mass and volume of sphere - diameter measurements of sphere   IPK & optical interferometer

1 Kg single-crystal silicon sphere the roundest man-made object in the world

Vm =Mm

ρ

NA =nMm

ρa3

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Avogadro Project Metrologia 48 (2011) S1 PRL 106 (2011) 030801

The float-zone 28 Si crystal & its cutting plan

To determine density two spheres (AVO28-S5

and AVO28-S8) were manufactured from the

two bulges

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Avogadro Project Metrologia 48 (2011) S1 PRL 106 (2011) 030801

NA = 6.022 140 78 (18) × 10 23 mol-1 Relative uncertainty 3 × 10 –8

NAh = 3.990 312 717 6 J s mol-1 Relative uncertainty 7× 10 –10

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Results of determination of h Metrologia 51 (2014) R21

  Watt balance (WB)

  Avogadro project (IAC)

  Significant discrepancies

  Postponed till data are consistent

  Could be adopted in 2018

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Summary and Outlook   Activities of everyday life affected directly or indirectly by mass measurement   Uniform standards are needed   In 2015 the kilogram remains as the only SI base unit defined by artifact   In constant danger of being destroyed and damaged

  Instabilities in definition of Kg propagate to other SI base units   ampere, mole and candela

  Propagates to to derived quantities   density, force, pressure

  Redefinition of Kg in terms of fundamental constant of nature h   Standards need to be met: relative uncertainties below 2 × 10-8

  Two types of experiments can reach required precision   watt balance and Avogadro project

  Significant discrepancies between available experimental values as of 2014   Redefinition of the unit of mass postponed till data are consistent   Could be adopted in 2018…

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metre [m] – distance

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second

second [s] – time

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom

ampere [A] - electric current

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10–7 newton per metre of length

SI Base Units

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kelvin [K] - temperature

The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water

mole [mol] - amount of substance

1.  The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12

2.  When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles

candela [cd] – luminous intensity

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian

SI Base Units

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SI Derived Units Name Symbol Quantity SI Base Unit

newton N force 1 N = 1 kg m s-2

pascal Pa pressure 1 Pa = kg m－1 s－2

joule J energy 1 J = 1 kg m2 s-2

watt W power 1 W = kg m2 s－3

coulomb C electric charge 1 C = s A

volt V voltage 1 V = kg m2 s－3 A－1

tesla T magnetic field 1 T = kg s－2 A－1

weber Wb magnetic flux 1 Wb = kg m2 s－2 A－1

ohm Ω electrical resistance 1 Ω = 1 kg m2 s－3 A－2